It is often claimed (most recently by Michael Friedman) that Kant intended to justify Newton’s most fundamental claims expressed in the Principia, such as his laws of motion and the law of universal gravitation. In this article, I argue that the differences between Newton’s laws of motion and Kant’s laws of mechanics are not superficial or merely apparent. Rather, they reflect fundamental differences in their respective projects. This point can be seen especially clearly by considering the nature of the various (...) projects undertaken in Germany prior to Kant that discuss the laws of motion. Wolff and his followers qua metaphysicians were especially interested in providing nonempirical justifications of their laws of motion as well as an intelligible account of the fundamental properties of bodies in terms of substance, accident, and force. Maupertuis and Euler, despite often being seen as Newtonians, both drew on traditions other than Newton’s. Physics textbooks (by figures such as Erxleben, Karsten, ‘s Gravesande, and Musschenbroek) vary considerably in their aims, but in none of these cases is Newton’s main argument of the Principia presented. In light of the fact that these projects are distinct in significant ways from Newton’s project, the differences between Newton’s laws of motion and Kant’s laws of mechanics are most likely not merely apparent but reflect the fact that Kant, too, was pursuing a project fundamentally distinct from Newton’s. (shrink)

This article aims to interpret Leibniz’s dynamics project through a theory of the causation of corporeal motion. It presents an interpretation of the dynamics that characterizes physical causation as the structural organization of phenomena. The measure of living force by mv2 must then be understood as an organizational property of motion conceptually distinct from the geometrical or otherwise quantitative magnitudes exchanged in mechanical phenomena. To defend this view, we examine one of the most important theoretical discrepancies of Leibniz’s dynamics with (...) classical mechanics, the measure of vis viva as mv2 rather than ½ mv2. This “error”, resulting from the limits of Leibniz’s methodology, reveals the systematic role of this quantity mv2 in the dynamics. In examining the evolution of the quantity mv2 in the refinement of the force concept from potentia to actio, I argue that Leibniz’s systematic limitations help clarify dynamical causality as neither strictly metaphysical nor mechanical but a distinct level of reality to which Leibniz dedicates the “dynamica” as “nova scientia”. (shrink)

Yves Simonin, a rather obscure professor of hydrography in Bayonne, submitted five scientific papers to the Paris Academy of Sciences between 1738 and 1740, which only survive in the original manuscript versions. The topics Simonin deals with in these texts are essentially three: the rectification of navigation charts of the Southern Sea, the shape of the Earth, and the heliocentric theory. Far from acknowledging Simonin's contribution to the ongoing academic debate as a valuable one, the institution systematically rejected his work. (...) In this paper, I first provide a critical analysis of Simonin's manuscripts. As I argue, their originality lies in the adoption of the perspective of a practitioner of and expert in navigational techniques. I then investigate the reasons behind the Academy's negative reception of Simonin's papers, casting light on the expertise required to participate in academic debates in the mid-18th century, and on the limits set by the institution to the possibility of external intervention. (shrink)

Newton certainly regarded his second law of motion in the Principia as a fundamental axiom of mechanics. Yet the works that came after the Principia, the major treatises on the foundations of mechanics in the eighteenth century—by Varignon, Hermann, Euler, Maclaurin, d’Alembert, Euler (again), Lagrange, and Laplace—do not record, cite, discuss, or even mention the Principia’s statement of the second law. Nevertheless, the present study shows that all of these scientists do in fact assume the principle that the Principia’s second (...) law asserts as a fundamental axiom in their mechanics. (For what that second law asserts, we rely on Newton’s own testimony.) Some, like Varignon and Hermann, assume the axiom implicitly, apparently unaware that any assumption is being made, while others, like Maclaurin and Euler, assume the axiom explicitly, apparently unaware that the assertion assumed is the second law as Newton himself understood it. But in every case these scientists employ the principle asserted by the Principia’s second law fundamentally, unaware that they should be citing Neutonus, Prin., Phil. Nat. Math., Lex II. (shrink)

This paper focuses on the link between systems criticism and anti-mathematicism in the French-speaking philosophical literature of the mid-18thcentury. Moving from Condillac’s omissions to the exemplary cases of Diderot and Buffon—as well as considering Formey’s crucial remarks—I reconsider the complex relationship that the authors of the French Enlightenment have with the Newtonian model. Finally, I inquire into the fate awaiting both mathematics and systems in this context after 1750.

D’Alembert a plusieurs fois exprimé sa conviction qu’une chaîne unissait tous les êtres naturels. C’est un thème métaphysique traditionnel, qui revient à la mode vers 1750, et qui manifeste l’influence de Leibniz. S’agit-il d’une chaîne des êtres ou des sdences? D’Alembert s’inspire de Descartes dans la description de l’ordre du savoir.

Euclidean geometry, statics, and classical mechanics, being in some sense the simplest physical theories based on a full-fledged mathematical apparatus, are well suited to a historico-philosophical analysis of the way in which a physical theory differs from a purely mathematical theory. Through a series of examples including Newton’s Principia and later forms of mechanics, we will identify the interpretive substructure that connects the mathematical apparatus of the theory to the world of experience. This substructure includes models of experiments, models of (...) measurement, and modular connections with partial theories. It evolves during the life of a theory as physicists learn how to apply it in various contexts. It should nevertheless be regarded as an integral part of a genuine physical theory since the theory would otherwise degenerate into pure mathematics. (shrink)

In French mechanical treatises of the nineteenth century, Newton’s second law of motion was frequently derived from a relativity principle. The origin of this trend is found in ingenious arguments by Huygens and Laplace, with intermediate contributions by Euler and d’Alembert. The derivations initially relied on Galilean relativity and impulsive forces. After Bélanger’s Cours de mécanique of 1847, they employed continuous forces and a stronger relativity with respect to any commonly impressed motion. The name “principle of relative motions” and the (...) very idea of using this principle as a constructive tool were born in this context. The consequences of Poincaré’s and Einstein’s awareness of this approach are analyzed. Lastly, the legitimacy and significance of a relativity-based derivation of Newton’s second law are briefly discussed in a more philosophical vein. (shrink)